Questions: Eleven people arrive at the ticket counter of Starlite Cinema at the same time. In how many ways can they line up to purchase their tickets? ways

Eleven people arrive at the ticket counter of Starlite Cinema at the same time. In how many ways can they line up to purchase their tickets? ways

Transcript text: Eleven people arrive at the ticket counter of Starlite Cinema at the same time. In how many ways can they line up to purchase their tickets? $\square$ ways Need Help? Read It

Solution

Solution Steps

To determine the number of ways eleven people can line up, we need to calculate the number of permutations of 11 distinct individuals. This is given by the factorial of 11, denoted as 11!.

Step 1: Determine the Number of Permutations

To find the number of ways eleven people can line up, we calculate the number of permutations of 11 distinct individuals. This is given by the factorial of 11, denoted as $11!$.

Step 2: Calculate the Factorial

The factorial of a number $n$, denoted as $n!$, is the product of all positive integers less than or equal to $n$. Therefore, for $n = 11$:

\[ 11! = 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]

Step 3: Compute the Result

Calculating the above expression gives:

\[ 11! = 39,916,800 \]